A note on costs minimization with stochastic target constraints

Yan Dolinsky, Benjamin Gottesman, Ori Gurel-Gurevich

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We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi-linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.

Original languageAmerican English
Article number11
JournalElectronic Communications in Probability
StatePublished - 2020

Bibliographical note

Funding Information:
Acknowledgments. We would like to thank the anonymous reviewers for their suggestions and comments which improved the paper. We also would like to thank Peter Bank, Asaf Cohen and Ross Pinsky for valuable discussions. This research was partially supported by the ISF grant no 160/17 and the ISF grant no 1707/16.

Publisher Copyright:
© 2020, Institute of Mathematical Statistics. All rights reserved.


  • Backward stochastic differential equations
  • Optimal stochastic control


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